Gas generators have to be small in size and must open up the possibility of fastening the gas-directing part, adjoining them in the direction of flow, in a simple and gas-tight manner to the gas generators. In the region of the fastening section the gas generator with the connected gas-directing part is likewise to be small in size, which, however, is not always possible, because in this region also gas-directing channels with a certain minimum cross-section must be present, so that the gas also arrives quickly to the vehicle occupant restraint system (preferably gas bag or belt tensioner). The gas-directing part can preferably be a gas-directing pipe or gas lance leading to a vehicle occupant restraint system. However, the vehicle occupant restraint system can also be fastened directly to the gas generator, e.g. the gas bag can be clamped to the gas generator in the region of its inflation orifice.